Gödel, Escher, Bach: Recursive Thinking


“butterfly”, by M C Escher

Curran Kelleher rocks recursion:

Gödel, Escher, Bach – Lecture 2: Part 1 of 8

Gödel, Escher, Bach – Lecture 2: Part 2 of 8

Gödel, Escher, Bach – Lecture 2: Part 3 of 8

Gödel, Escher, Bach – Lecture 2: Part 4 of 8

Gödel, Escher, Bach – Lecture 2: Part 5 of 8

Gödel, Escher, Bach – Lecture 2: Part 6 of 8

Gödel, Escher, Bach – Lecture 2: Part 7 of 8

Gödel, Escher, Bach – Lecture 2: Part 8 of 8

This lecture series is available through MIT’s Open Courseware


Socrates and the Death of Scientific Optimism


From an article by Jonathan Amos, “Stonehenge design was ‘inspired by sounds'”

Friedrich Wilhelm Nietzsche, “The Birth of Tragedy, Out of the Spirit of Music”

And now we should not conceal from ourselves what lies hidden in the womb of this Socratic culture! An optimism that thinks itself all-powerful! Well, people should not be surprised when the fruits of this optimism ripen, when a society that has been thoroughly leavened with this kind of culture, right down to the lowest levels, gradually trembles with an extravagant turmoil of desires, when the belief in earthly happiness for everyone, when faith in the possibility of such a universal knowledge culture gradually changes into the threatening demand for such an Alexandrian earthly happiness, into the plea for a Euripidean deus ex machina! People should take note: Alexandrian culture requires a slave class in order to be able to exist over time, but with its optimistic view of existence, it denies the necessity for such a class and thus, when the effect of its beautiful words of seduction and reassurance about the “dignity of human beings” and the “dignity of work” has worn off, it gradually moves towards a horrific destruction. There is nothing more frightening than a barbarian slave class which has learned to think of its existence as an injustice and is preparing to take revenge, not only for itself, but for all generations. In the face of such threatening storms, who dares appeal with sure confidence to our pale and exhausted religions, which themselves in their foundations have degenerated into scholarly religions, so that myth, the essential pre-condition for every religion, is already paralyzed everywhere, and even in this area that optimistic spirit which we have just described as the germ of destruction of our society has gained control.

While the disaster slumbering in the bosom of theoretical culture gradually begins to worry modern man, while he, in his uneasiness, reaches into the treasure of his experience for ways to avert the danger, without himself having any real faith in these means, and while he also begins to have a premonition of the particular consequences for him, some great wide-ranging natures have, with an incredible circumspection, known how to use the equipment of science itself to set out the boundaries and restricted nature of knowledge generally and, in the process, decisively to deny the claim of science to universal validity and universal goals. Given proofs like this, the delusion which claims that with the help of causality it can fathom the innermost essence of things has for the first time become recognized for what it is. The immense courage and wisdom of Kant and Schopenhauer achieved the most difficult victory, the victory over the optimism lying concealed in the essential nature of logic, which is, in turn, the foundation of our culture. While this logic, based on aeternae veritates [eternal truths] which it did not consider open to objection, believed that all the riddles of the world could be recognized and resolved and had treated space, time, and causality as totally unconditional laws with the most universal validity, Kant showed how these really served only to raise mere appearance, the work of Maja, to the single, highest reality and to set it in place of the innermost and true essence of things and thus to make true knowledge of this essence impossible, that is, in the words of Schopenhauer, to get the dreamer to sleep even more soundly (World as Will and Idea, I, 498). With this recognition there is introduced a culture which I venture to describe as a tragic culture. Its most important distinguishing feature is that wisdom replaces science as the highest goal, a wisdom which, undeceived by the seductive diversions of science, turns its unswerving gaze onto the all-encompassing picture of the world and, with a sympathetic feeling of love, seeks in that world to grasp eternal suffering as its own suffering. Let us picture for ourselves a generation growing up with this fearlessness in its gaze, with this heroic push into what is tremendous; let us picture for ourselves the bold stride of these dragon slayers, the proud audacity with which they turn their backs on all the doctrines of weakness associated with that optimism, in order “to live with resolution,” fully and completely. Would it not be necessary that the tragic man of this culture, having trained himself for what is serious and frightening, desire a new art, the art of metaphysical consolation, the tragedy, as his own personal Helen of Troy, and to have to cry out with Faust:

With my desire’s power, should I not call
Into this life the fairest form of all?

However, now that Socratic culture has been shaken on two sides and can hang onto the sceptre of its infallibility only with trembling hands, first of all by the fear of its own consequences, which it is definitely beginning to sense and, in addition, because it is itself no longer convinced with that earlier naive trust of the eternal validity of its foundations, it’s a sorry spectacle how the dance of its thinking constantly dashes longingly after new forms in order to embrace them and then how, like Mephistopheles with the seductive Lamias, it suddenly, with a shudder, lets them go again. That is, in fact, the characteristic mark of that “fracture” which everyone is in the habit of talking about as the root malady of modern culture, that theoretical man is afraid of his own consequences and, in his dissatisfaction, no longer dares to commit himself to the fearful ice currents of existence. He runs anxiously up and down along the shore. He no longer wants to have anything completely, any totality with all the natural cruelty of things. That’s how much the optimistic way of seeing things has mollycoddled him. At the same time he feels how a culture which has been built on the principle of science must collapse when it begins to become illogical, that is, when it begins to run back once it is faced with its own consequences. Our art reveals this general distress: in vain people use imitation to lean on all the great productive periods and natures; in vain they gather all “world literature” around modern man to bring him consolation and place him in the middle of artistic styles and artists of all ages, so that he may, like Adam with the animals, give them a name. But he remains an eternally hungry man, the “critic” without joy and power, the Alexandrian man, who is basically a librarian and copy editor and goes miserably blind from the dust of books and printing errors.